Can someone help me solve for this missing side?

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Answer 1 · 2018-02-28T07:49:18

Fourth option is the right choice.

$c = 24.34$ $c=24.34$

First you need to apply the sine's law to calculate the measure of angle $m ∠ B$ $m\angle B$ .

$\frac{a}{sin (A^{\circ})} = \frac{b}{sin (B^{\circ})}$ $a/Sin(A^{\circ})=b/Sin(B^{\circ})$

By putting the values and solving for $m ∠ B$ $m\angle B$ , you will get:

$m ∠ B = {22.32}^{\circ}$ $m\angle B=22.32^{\circ}$

Now to find the value of $c$ $c$ , we need to apply the cosine's law, which is stated as:

$c = a^{2} + b^{2} - 2 a b cos (C^{\circ})$ $c=a^2+b^2-2abCos(C^{\circ})$

To get the missing angle $m ∠ C$ $m\angle C$ , we need to apply the theorem that sum of all the angles in a triangle is $180^{\circ}$ $180^{\circ}$

So, that we get:

$m ∠ C = {138.68}^{\circ}$ $m\angle C=138.68^{\circ}$

Now, by applying the cosine's law, you will get:

$c = 24.34$ $c=24.34$

That's it!